In this section we describe a constructive method of polarization kernel search, which in many cases improves the lower bound on the maximal rate of polarization \(E_l\)  achievable by \(l \times l\)  polarization kernel, i.e. \(E_l = \max _{K \in \mathbb {F}_2^{l \times l}} E(K)\) . Lower and upper bounds on \(E_l\)  for some \(l\)  were derived in [1]}, [2]} and
[3]} together with explicit kernels achieving lower bounds.
